Question

Each summer Primo Pizza and Pizza Supreme compete to see who has the larger summer profit. Let p(x) represent Primo Pizza's profit (in dollars) x days after June 1. Let s(x) represent Pizza Supreme's profit (in dollars) x days after June 1.

c. Suppose Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.

i) Write a function formula for p using the function s

. p(x)=


ii) Write a function formula for s using the function p

s(x)=

.

Answer 1

Primo Pizza's profit function p(x) is related to Pizza Supreme's profit function s(x) such that p(x) = s(x + 4). Similarly, s(x) = p(x - 4). These functions express the profits in terms of each other with a 4-day shift in time.

Step-by-step explanation:

Given that Primo Pizza's profit p(x) on a given day is the same as Pizza Supreme's profit s(x) 4 days later, we can write the following relationships between the two functions:

• p(x) = s(x + 4)

• s(x) = p(x - 4)

This implies that to find Primo Pizza's profit on the x-th day, we need to find out what Pizza Supreme's profit was on the (x + 4)-th day. Conversely, to compute Pizza Supreme's profit on the x-th day, we need to find Primo Pizza's profit 4 days earlier, on the (x - 4)-th day.

Answer 2

a)

i) p(x) = 1.4 s(x)

ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4

b)

i) p(x) = [s(x) + 200]

ii) s(x) = [p(x) - 200]

c)

i) p(x) = s(x+4)

ii) s(x) = p(x-4)

Step-by-step explanation:

Complete Question

Each summer Primo Pizza and Pizza Supreme compete to see who has the larger summer profit. Let p(x) represent Primo Pizza's profit (in dollars) x days after June 1. Let s(x) represent Pizza Supreme's profit (in dollars) x days after June 1.

a) Suppose Primo Pizza's profit each day is 1.4 times as large as the profit of Pizza Supreme

i. Write a function formula for p using the function s.

ii. Write a function formula for s using the function p.

b) Suppose Primo Pizza's profit each day is $200 more than the profit of Pizza Supreme.

i) Write a function formula for p using the function s.

ii) Write a function formula for s using the function p.

c) Suppose Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.

i) Write a function formula for p using the function s.

ii) Write a function formula for s using the function p.

The profits per day for Primo Pizza, x days after June 1 = p(x)

The profits per day for Supreme Pizza, x days after June 1 = s(x)

a) Primo Pizza's profits per day is 1.4 times that of Supreme Pizza's per day.

Primo Pizza's profits per day, x days after June 1 = p(x)

Supreme Pizza's profit per day, x days after June 1 = s(x)

i) p(x) = 1.4 s(x)

ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4

b) Primo Pizza profits per day is $200 more than that of Supreme Pizza

Primo Pizza's profits per day, x days after June 1 = p(x)

Supreme Pizza's profit per day, x days after June 1 = s(x)

i) p(x) = [s(x) + 200]

ii) s(x) = [p(x) - 200]

c) Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.

Primo Pizza's profits per day, x days after June 1 = p(x)

Supreme Pizza's profit per day, x days after June 1 = s(x)

Supreme Pizza's profit per day, 4 days later = s(x+4)

So,

i) p(x) = s(x+4)

ii) This means that Supreme Pizza's profit per day is the same as Primo Pizza's profit per day four days ago.

Primo Pizza's profit per day four days ago = p(x-4)

So,

s(x) = p(x-4)

Hope this Helps!!!